J. P. Lynch, K. Diamanti, and C. Soutis, A Summary Review of Wireless Sensors and Sensor Networks for Structural Health Monitoring. The Shock and Vibration Digest Structural health monitoring techniques for aircraft composite structures, Progress in Aerospace Sciences, pp.91-128, 2006.

Z. Xiaoliang, Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. Defect detection, localization and growth monitoring, Smart Materials and Structures, vol.164, issue.4, p.1208, 2007.

I. Jeong-beom, C. Fu-kuo, J. Ihn, F. Chang, and W. H. Leong, Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: I Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: II. Validation using riveted joints and repair patches, Structural health monitoring using scanning laser vibrometry: III. Lamb waves for fatigue crack detection. Smart Materials and Structures, pp.609-621, 2004.

W. J. Staszewski, Fatigue damage and sensor development for aircraft structural health monitoring. Theoretical and Applied Fracture Mechanics Maintenance Policies for Stochastically Failing Equipment: A Survey Optimal maintenance models for systems subject to failure?A Review A survey of maintenance models for multi-unit systems Cost Optimization of Periodic Preventive Maintenance, Structural health monitoring using scanning laser vibrometry: I. Lamb wave sensing. Smart Materials and Structures Optimal policy of continuous and discrete replacement with minimal repair at failure. Naval Research Logistics Quarterly, pp.251-274, 1965.

A. Tam, W. Chan, P. , J. Baldin, A. E. Baidin et al., Optimal maintenance intervals for a multi-component system. Production Planning and Control Condition based maintenance in chemical and chemical fiber industries. Monitoring Diagnostics in the Industry Congress The reliability of condition-based maintenance Condition-based maintenance: A powerful tool for modern management. Terotecnica I Condition-based maintenance implementation and experiences, pp.17-769, 1973.

X. Zhou, L. Xi, L. , and J. , Reliability-centered predictive maintenance scheduling for a continuously monitored system subject to degradation. Reliability Engineering & System Safety [21] Van Horenbeek, A. and Pintelon, L., A dynamic predictive maintenance policy for complex multi-component systems, Reliability Engineering & System Safety, vol.9222, issue.120, pp.530-534, 2007.

M. Traore, A. Chammas, E. Duviella, K. Nguyen, P. Do et al., Supervision and prognosis architecture based on dynamical classification method for the predictive maintenance of dynamical evolving systems Multi-level predictive maintenance for multi-component systems A predictive maintenance policy with imperfect monitoring, Reliability Engineering & System Safety, pp.120-131, 2010.

H. Li, Improving rail network velocity: A machine learning approach to predictive maintenance. Transportation Research Part C: Emerging Technologies, pp.17-26, 2014.

D. Bansal, D. J. Evans, and B. S. Jones, BJEST: A reverse algorithm for the real-time predictive maintenance system Application of Bayesian networks in prognostics for a new Integrated Vehicle Health Management concept, International Journal of Machine Tools and Manufacture Expert Systems with Applications, issue.107, pp.46-85, 2006.

M. Tan, C. Raghavan, N. Deloux, E. Castanier, B. Bérenguer et al., Predictive maintenance policy for a gradually deteriorating system subject to stress Predictive Maintenance Management Using Sensor-Based Degradation Models Predictive maintenance policy based on process data. Chemometrics and Intelligent Laboratory Systems Application of infrared thermography for predictive/preventive maintenance of thermal defect in electrical equipment Vibration monitoring for defect diagnosis of rolling element bearings as a predictive maintenance tool: Comprehensive case studies Wireless sensors for predictive maintenance of rotating equipment in research reactors Selection of diagnostic techniques and instrumentation in a predictive maintenance program. A case study, A framework to practical predictive maintenance modeling for multi-state systems. Reliability Engineering & System Safety IEEE Transactions on Systems, Man, and Cybernetics -Part A: Systems and Humans 45th CIRP Conference on Manufacturing Systems 2012On a Predictive Maintenance Platform for Production Systems. Procedia CIRP International Workshop on Information and Electronics EngineeringAircraft Maintenance Decision System Based on Real-time Condition Monitoring. Procedia Engineering, pp.93-1138, 2005.

M. C. Garcia, M. A. Sanz-bobi, and J. Del-pico, SIMAP: Intelligent System for Predictive Maintenance: Application to the health condition monitoring of a windturbine gearbox, pp.552-568, 2006.

D. Bansal, D. J. Evans, B. Jones, and J. Lee, A real-time predictive maintenance system for machine systems An evaluation system of the setting up of predictive maintenance programmes Industrial Big Data Analytics and Cyber-physical Systems for Future Maintenance & Service Innovation Prognostic modelling options for remaining useful life estimation by industry Practical options for selecting data-driven or physics-based prognostics algorithms with reviews. Reliability Engineering & System Safety A review of diagnostics and prognostics of low-speed machinery towards wind turbine farm-level health management Prognostics and health management design for rotary machinery systems?Reviews, methodology and applications, Mechanical Systems and Signal Processing, pp.44-51, 2004.

A. K. Jardine, D. Lin, and D. Banjevic, A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, pp.1483-1510, 2006.

X. Si, Remaining useful life estimation ? A review on the statistical data driven approaches Particle filter-based prognostics: Review, discussion and perspectives. Mechanical Systems and Signal Processing Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life. Reliability Engineering & System Safety Data-driven prognostic method based on Bayesian approaches for direct remaining useful life prediction, European Journal of Operational Research Journal of Intelligent Manufacturing, vol.21351, issue.103, pp.1-14, 2011.

L. Son and K. , Remaining useful life estimation based on stochastic deterioration models: A comparative study Reliability Engineering & System Safety A recursive Bayesian approach for fatigue damage prognosis: An experimental validation at the reliability component level. Mechanical Systems and Signal Processing Integration of structural health monitoring and fatigue damage prognosis Prediction of remaining useful life for fatigue-damaged structures using Bayesian inference A reliability-based framework for fatigue damage prognosis of composite aircraft structures, Mechanical Systems and Signal Processing Probabilistic Engineering Mechanics, pp.165-175, 2012.

J. Sun, Prognostics uncertainty reduction by fusing on-line monitoring data based on a state-space-based degradation model. Mechanical Systems and Signal Processing A particle filtering and kernel smoothing-based approach for new design component prognostics, Reliability Engineering & System Safety, vol.4558, issue.134, pp.396-407, 2014.

E. Zio, G. Peloni, and P. Baraldi, Particle filtering prognostic estimation of the remaining useful life of nonlinear components, Mechanical Systems and Signal Processing, pp.403-409, 2011.
DOI : 10.1016/j.ress.2010.08.009
URL : https://hal.archives-ouvertes.fr/hal-00609502

X. S. Si, An Adaptive Prognostic Approach via Nonlinear Degradation Modeling: Application to Battery Data, IEEE Transactions on Industrial Electronics, vol.62, issue.8, pp.5082-5096, 2015.
DOI : 10.1109/TIE.2015.2393840

X. S. Si, Estimating Remaining Useful Life With Three-Source Variability in Degradation Modeling The unscented Kalman filter for nonlinear estimation AS-SPCC. The IEEE A general method for approximating nonlinear transformations of probability distributions Aerodynamic parameter estimation for high-performance aircraft using extended Kalman filtering, Adaptive Systems for Signal Processing, Communications, and Control Symposium 20th Atmospheric Flight Mechanics Conference and Jategaonkar, R., Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter. Aerospace Science and Technology, pp.167-190, 1995.

S. Aksoy, A. Muhurcu, and H. Kizmaz, State and parameter estimation in induction motor using the Extended Kalman Filtering algorithm, Modern Electric Power Systems (MEPS), 2010 Proceedings of the International Symposium, 2010.

S. S. Bisht, M. P. Singh, and L. Alfonso, An adaptive unscented Kalman filter for tracking sudden stiffness changes Mechanical Systems and Signal Processing Mobile robot localization via EKF and UKF: A comparison based on real data Estimation of hydrodynamic coefficients of a test-bed AUV-SNUUV I by motion test. in OCEANS '02 MTS/IEEE Extended Kalman Filter for prognostic of Proton Exchange Membrane Fuel Cell, 72] Julier, S.J. and Uhlmann, J.K. New extension of the Kalman filter to nonlinear systems. in AeroSense'97 International Society for Optics and Photonics, pp.181-195, 1997.

M. C. Vandyke, J. L. Schwartz, C. D. Hall, J. L. Crassidis, F. L. Markley et al., Unscented Kalman filtering for spacecraft attitude state and parameter estimation Unscented Filtering for Spacecraft Attitude Estimation Process monitoring and parameter estimation via unscented Kalman filtering Journal of Loss Prevention in the Process Industries, A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems based on Extended and Sigma Point Kalman Filters. Navigation, pp.536-542, 2003.

W. Jan, Filtering and prediction techniques for model-based prognosis and uncertainty management. in 2010 Prognostics and System Health Management Conference Prognostics 101: A tutorial for particle filter-based prognostics algorithm using Matlab. Reliability Engineering & System Safety Novel metrics and methodologies for the verification and validation of prognostic algorithms Lithium-ion battery life prognostic health management system using particle filtering framework, Aerospace Conference Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, pp.161-169, 2005.

M. Jouin, Prognostics of PEM fuel cell in a particle filtering framework Prognostics of Proton Exchange Membrane Fuel Cell stack in a particle filtering framework including characterization disturbances and voltage recovery, Prognostics and Health Management (PHM), 2014 IEEE Conference on, pp.481-494, 2014.

J. K. Kimotho, T. Meyer, and W. Sextro, PEM fuel cell prognostics using particle filter with model parameter adaptation, 2014 International Conference on Prognostics and Health Management, 2014.
DOI : 10.1109/ICPHM.2014.7036406

B. Zhang, A multi-fault modeling approach for fault diagnosis and failure prognosis of engineering systems. in Annual conference of the prognostics and health management society, 2009.

L. Guo, Comparison of resampling algorithms for particle filter based remaining useful life estimation Lithium-ion battery state of health monitoring and remaining useful life prediction based on support vector regression-particle filter Precognitive maintenance and probabilistic assessment of tool wear using particle filters, 2014 International Conference on Prognostics and Health Management IECON 2013 -39th Annual Conference of the IEEE Industrial Electronics Society. 2013. [89] Arulampalam, M.S., et al., A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, pp.114-123, 2002.

G. Yi, G. Shesheng, Y. , and G. , Improved regularized particle filter algorithm for SINS/SAR integrated navigation Implementing particle filters with Metropolis-Hastings algorithms, 2010 International Conference on Computer Application and System Modeling Region 5 Conference: Annual Technical and Leadership Workshop, 2004.

T. Li, T. P. Sattar, and S. Sun, Deterministic resampling: Unbiased sampling to avoid sample impoverishment in particle filters, Signal Processing, vol.92, issue.7, pp.1637-1645, 2012.
DOI : 10.1016/j.sigpro.2011.12.019

C. Andrieu, N. D. Freitas, A. Doucet, J. D. Nordh, J. Choi et al., Sequential MCMC for Bayesian model selection. in Higher-Order Statistics Metropolis-hastings improved particle smoother and marginalized models A Comparison Study of Methods for Parameter Estimation in the Physics-based Prognostics Prediction of remaining useful life for fatigue-damaged structures using Bayesian inference, Proceedings of the IEEE Signal Processing Workshop on Signal Processing Conference (EUSIPCO) 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 2012, pp.96-588, 1999.

C. Andrieu, An Introduction to MCMC for Machine Learning Technical Note?Nonlinear Least Squares Estimation of New Product Diffusion Models Algorithms for the Solution of the Nonlinear Least-Squares Problem, Machine Learning, pp.5-43, 1978.

B. A. Boukamp, A Nonlinear Least Squares Fit procedure for analysis of immittance data of electrochemical systems, Solid State Ionics, vol.20, issue.1, pp.31-44, 1986.
DOI : 10.1016/0167-2738(86)90031-7

J. J. Moré, The Levenberg-Marquardt algorithm: implementation and theory, in Numerical analysis, pp.105-116, 1978.

M. S. Grewal and A. P. Andrews, Kalman filtering: Theory and Practice with MATLAB, 2014.
DOI : 10.1002/9781118984987

E. Choi, Onboard orbit determination using GPS observations based on the unscented Kalman filter Advances in Space Research, pp.46-1440, 2010.

C. E. Harris, Analytical Methodology for Predicting Widespread Fatigue Damage Onset in Fuselage Structure, Journal of Aircraft, vol.1, issue.5, pp.307-317, 1998.
DOI : 10.1111/j.1460-2695.1994.tb00242.x

J. R. Mohanty, B. B. Verma, R. , and P. K. , Prediction of fatigue crack growth and residual life using an exponential model: Part I (constant amplitude loading), International Journal of Fatigue, vol.31, issue.3, pp.31-418, 2009.
DOI : 10.1016/j.ijfatigue.2008.07.015

K. Nilsson, Elasto-plastic models for interaction between a major crack and multiple small cracks, FAA-NASA Symposium on the Continued Airworthiness of Aircraft Structures, 1996.

L. Molent and S. A. Barter, A comparison of crack growth behaviour in several full-scale airframe fatigue tests, International Journal of Fatigue, vol.29, issue.6, pp.29-1090, 2007.
DOI : 10.1016/j.ijfatigue.2006.09.015

P. Paris and F. Erdogan, A Critical Analysis of Crack Propagation Laws, Journal of Basic Engineering, vol.85, issue.4, pp.528-533, 1963.
DOI : 10.1115/1.3656900

M. T. Sabet, S. Pouria, and M. Zarini, Extended and Unscented Kalman filters for parameter estimation of an autonomous underwater vehicle. Ocean Engineering, pp.329-339, 2014.

B. Huang and X. Du, Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation, Reliability Engineering & System Safety, vol.93, issue.2, pp.325-336, 2008.
DOI : 10.1016/j.ress.2006.10.021

J. W. Bristow and P. E. Irving, Safety factors in civil aircraft design requirements. Engineering Failure Analysis, pp.459-470, 2007.

G. Cavallini and R. Lazzeri, A probabilistic approach to fatigue risk assessment in aerospace components, Engineering Fracture Mechanics, vol.74, issue.18, pp.74-2964, 2007.
DOI : 10.1016/j.engfracmech.2006.04.034

A. T. Nelson and E. A. Wan, A two-observation Kalman framework for maximum-likelihood modeling of noisy time series, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227), 1998.
DOI : 10.1109/IJCNN.1998.687253

E. A. Wan and A. T. Nelson, Dual Extended Kalman Filter Methods, Kalman Filtering and Neural Networks, pp.123-173, 2002.
DOI : 10.1002/0471221546.ch5

M. D. Mckay, R. J. Beckman, and W. J. Conover, A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics, vol.21, issue.2, pp.239-245, 1979.

A. M. Hasofer and N. C. Lind, Exact and invariant second-moment code format(for reliability analysis in multivariate problems), Engineering Mechanics Division Journal, vol.100, pp.111-121, 1974.

M. Hohenbichler, New light on first-and second-order reliability methods. Structural Safety, pp.267-284, 1987.

D. Xiangjun and T. Jiang, Reliability prediction based on degradation measure distribution and wavelet neural network, Proceedings of the IEEE 2012 Prognostics and System Health Management Conference (PHM-2012 Beijing), 2012.
DOI : 10.1109/PHM.2012.6228782

H. L. Wu, Y. Zhong, Y. , and J. , An improved reliability prediction model based on BP network, Computer and Automation Engineering (ICCAE) The 2nd International Conference on, 2010.

N. Karunanithi, D. Whitley, and Y. K. Malaiya, Using neural networks in reliability prediction, IEEE Software, vol.9, issue.4, pp.53-59, 1992.
DOI : 10.1109/52.143107

R. M. Gorguluarslan and S. Choi, Predicting Reliability of Structural Systems Using Classification Method, Volume 2A: 33rd Computers and Information in Engineering Conference, 2013.
DOI : 10.1115/DETC2013-13323

L. N. Qin, Software reliability prediction model based on PSO and SVM, 2011 International Conference on Consumer Electronics, Communications and Networks (CECNet), 2011.
DOI : 10.1109/CECNET.2011.5768285

X. Wu, Failure and reliability prediction of engine systems using iterated nonlinear filters based state-space least square support vector machine method, Optik - International Journal for Light and Electron Optics, vol.127, issue.3, pp.1491-1496, 2016.
DOI : 10.1016/j.ijleo.2015.11.024

Z. Xu, Y. Ji, and D. Zhou, Real-time Reliability Prediction for a Dynamic System Based on the Hidden Degradation Process Identification, IEEE Transactions on Reliability, vol.57, issue.2, pp.230-242, 2008.

A. Amin, L. Grunske, and A. Colman, An approach to software reliability prediction based on time series modeling, Journal of Systems and Software, vol.86, issue.7, pp.86-1923, 2013.
DOI : 10.1016/j.jss.2013.03.045

W. Peng and D. W. Coit, Reliability prediction based on degradation modeling for systems with multiple degradation measures. in Reliability and Maintainability, Annual Symposium -RAMS, 2004.

W. Zhao, T. Tao, and E. Zio, System reliability prediction by support vector regression with analytic selection and genetic algorithm parameters selection, Applied Soft Computing, vol.30, pp.792-802, 2015.
DOI : 10.1016/j.asoc.2015.02.026

K. Chen, Forecasting systems reliability based on support vector regression with genetic algorithms. Reliability Engineering & System Safety, pp.423-432, 2007.

W. Zhao, A dynamic particle filter-support vector regression method for reliability prediction, Reliability Engineering & System Safety, vol.119, pp.109-116, 2013.

M. Bazu, Fuzzy-Logic Reliability Predictions in Microtechnologies, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06), 2005.
DOI : 10.1109/CIMCA.2005.1631247

H. Haiyan, Z. De-zi, N. , and C. , Aeroengine Reliability Prediction Based on Fuzzy and Interval Number, Procedia Engineering, vol.99, pp.1284-1288, 2015.

D. Chen, C. Yao, and Z. Feng, Reliability Prediction Method of Hydraulic System by Fuzzy Theory, IFAC Proceedings Volumes, pp.457-462, 2013.
DOI : 10.3182/20130410-3-CN-2034.00009

J. Y. Yao, Modeling system based on fuzzy dynamic Bayesian network for fault diagnosis and reliability prediction, 2015 Annual Reliability and Maintainability Symposium (RAMS), 2015.
DOI : 10.1109/RAMS.2015.7105193

S. Yang, M. Lu, and L. Ge, Bayesian Network Based Software Reliability Prediction by Dynamic Simulation, 2013 IEEE 7th International Conference on Software Security and Reliability, 2013.
DOI : 10.1109/SERE.2013.24

L. Ching, T. , D. Shang, and C. , Reliability prediction using nondestructive accelerated-degradation data: case study on power supplies, IEEE Transactions on Reliability, vol.44, issue.4, pp.562-566, 1995.

Y. Wan, Thermal reliability prediction and analysis for high-density electronic systems based on the Markov process. Microelectronics Reliability, pp.182-188, 2016.

M. B. Cortie and G. G. Garrett, On the correlation between the C and m in the paris equation for fatigue crack propagation, Engineering Fracture Mechanics, vol.30, issue.1, pp.49-58, 1988.
DOI : 10.1016/0013-7944(88)90254-8

J. P. Benson and D. V. Edmonds, The relationship between the parameters C and m of Paris' law for fatigue crack growth in a low-alloy steel, Scripta Metallurgica, vol.12, issue.7, pp.12-645, 1978.
DOI : 10.1016/0036-9748(78)90278-8

Ö. G. B??-l??-r, The relationship between the parameters C and n of Paris' law for fatigue crack growth in a SAE 1010 steel, Engineering Fracture Mechanics, vol.36, issue.2, pp.361-364, 1990.

S. Pattabhiraman, Skipping unnecessary structural airframe maintenance using an on-board structural health monitoring system, Proceedings of the Institution of Mechanical Engineers, pp.549-560, 2012.
DOI : 10.1177/1748006X12459157

M. Remery, C. Mascle, and B. Agard, A new method for evaluating the best product end-of-life strategy during the early design phase, Journal of Engineering Design, vol.6, issue.7, pp.419-441, 2012.
DOI : 10.1016/S0377-2217(97)00147-1

M. Fajdiga, T. Jurejev?i?, and J. Kernc, Reliability Prediction in Early Phases of Product Design, Journal of Engineering Design, vol.2, issue.2, pp.107-128, 1996.
DOI : 10.1007/978-3-662-10446-0

P. Sriram, Synchronizing Condition-based Maintenance with Necessary Scheduled Maintenance, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2012.

Z. Q. Wang, A Prognostic-Information-Based Order-Replacement Policy for a Non-Repairable Critical System in Service, IEEE Transactions on Reliability, vol.64, issue.2, pp.721-735, 2015.
DOI : 10.1109/TR.2014.2371016

Y. Langeron, A. Grall, and A. Barros, A modeling framework for deteriorating control system and predictive maintenance of actuators, Reliability Engineering & System Safety, vol.140, issue.140, pp.22-36, 2015.
DOI : 10.1016/j.ress.2015.03.028

K. T. Huynh, A. Barros, and C. Berenguer, Multi-Level Decision-Making for The Predictive Maintenance of <formula formulatype="inline"><tex Notation="TeX">$k$</tex> </formula>-Out-of-<formula formulatype="inline"><tex Notation="TeX">$n$</tex> </formula>:F Deteriorating Systems, IEEE Transactions on Reliability, vol.64, issue.1, pp.94-117, 2015.
DOI : 10.1109/TR.2014.2337791

X. Guan, R. Jha, and Y. Liu, Model selection, updating, and averaging for probabilistic fatigue damage prognosis. Structural Safety, pp.242-249, 2011.

J. Scanlan, Cost modelling for aircraft design optimization, Journal of Engineering Design, vol.13, issue.3, pp.261-269, 2002.
DOI : 10.1080/09544820110108962

S. Tammineni, A knowledge-based system for cost modelling of aircraft gas turbines, Journal of Engineering Design, vol.3, issue.3, pp.289-305, 2009.
DOI : 10.2514/8.155

A. K. Kundu, Aircraft design, 2010.
DOI : 10.1017/CBO9780511844652

X. Huang, M. Torgeir, C. , and W. , An engineering model of fatigue crack growth under variable amplitude loading, International Journal of Fatigue, vol.30, issue.1, pp.2-10, 2008.
DOI : 10.1016/j.ijfatigue.2007.03.004

O. E. Wheeler, Spectrum Loading and Crack Growth, Journal of Basic Engineering, vol.94, issue.1, pp.181-186, 1972.
DOI : 10.1115/1.3425362